How to install localdb separately?

From MSDN

The primary method of installing LocalDB is by using the SqlLocalDB.msi program. LocalDB is an option when installing any SKU of SQL Server 2012 Express. Select LocalDB on the Feature Selection page during installation of SQL Server Express. There can be only one installation of the LocalDB binary files for each major SQL Server Database Engine version. Multiple Database Engine processes can be started and will all use the same binaries. An instance of the SQL Server Database Engine started as the LocalDB has the same limitations as SQL Server Express

Or you can download standalone SqlLocalDB.msi from the list of available downloads on the SQL Express downloading page

To locate localdb instance on your PC simply try to connect to (localdb)\Projects

If you downloaded SqlLocalDB.msi You can use silent install.

msiexec /i SqlLocalDB.msi /qn IACCEPTSQLLOCALDBLICENSETERMS=YES

Remember about administrative rights for installation !

Note for people who got SQL 2016. You do in fact need to choose "Express" during installation of SQL 2016 to choose "localDB" option. If you choose anything else (like Developer edition for example), "localDB" will not appear as option under "Shared features"

Developer Edition

SQL Express